Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions

TL;DR

This paper explores how time-reversal symmetry breaking in 4D QCD relates to phase transitions, domain wall dynamics, and dualities in 3D theories, revealing connections between 4D bulk properties and 3D boundary phenomena.

Contribution

It establishes a link between 4D QCD phase transitions and 3D Chern-Simons matter dualities, providing new insights into domain wall theories and their relation to 2+1 dimensional dualities.

Findings

First order transition at = in large mass limit

Domain walls support 3D d sigma models with Wess-Zumino terms

Connection between 4D bulk dynamics and 3D dualities

Abstract

We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $\theta$-parameter. For generic $m$ and $\theta$ the theory has a single gapped vacuum. However, as $\theta$ is varied through $\theta=\pi$ for large $m$ there is a first order transition. For $N_f=1$ the first order transition line ends at a point with a massless $\eta'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the $4d$ bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different $3d$ phases. These turn out to be the phases of the recently studied $3d$ Chern-Simons matter theories, thus relating the dynamics of QCD$_4$ and QCD$_3$, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless $4d$ theory has an $SU(N_f)$ sigma model, the domain wall theory at low (nonzero) mass supports a $3d$ massless $CP^{N_f-1}$ nonlinear $\sigma$-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.